The measure of an interior angle of a regular polygon is 150°. Find the number of sides in the polygon.

Steps to Solve

1. Formula for the measure of an interior angle

The formula for the measure of an interior angle of a regular $n$-sided polygon is:

$$ \text{Interior angle} = \frac{(n-2) \times 180^\circ}{n} $$

2. Substitute the given value

Given that the interior angle is $150^\circ$, substitute this value into the formula:

$$ 150 = \frac{(n-2) \times 180}{n} $$

3. Solve for $n$

Multiply both sides of the equation by $n$:

$$ 150n = (n-2) \times 180 $$

4. Expand the right side

$$ 150n = 180n - 360 $$

5. Rearrange the equation

Subtract $180n$ from both sides:

$$ 150n - 180n = -360 $$ $$ -30n = -360 $$

6. Isolate $n$

Divide both sides by $-30$:

$$ n = \frac{-360}{-30} $$ $$ n = 12 $$